Optimization of timber columns according to the constraints of NBR 7190:2022

Abstract

This work aims to apply structural optimization to timber columns in accordance with the NBR 7190-1 (ABNT, 2022) standard, seeking precise results in the design process. To achieve this, a Python routine was developed to determine the cross-sectional area and volume of the columns, considering the regulatory constraints. These calculations, where bending moments and axial forces are analyzed, will underpin parametric studies on the material's mass behavior under various conditions, such as wood species and length variation. The routine identifies the parameters to be optimized and applies the standard formulas to verify the structural condition, analyzing variables such as maximum slenderness, relative slenderness, and maximum flexural-compression stress. The optimization provides the optimal values for the cross-sectional area and volume of the column, which means that these obtained values are the ones that minimize the volume as a function, respecting the proposed standard constraints. It is observed that, in most cases, mass increases with incremental variations in the studied parameters, resulting in more robust column sections that are resistant to higher forces and loads.